Modified Bessel function of the first kind (Sympy, WMA)
BesselI[n, z]BesselI[0, 0]
BesselI[1.5, 4]
Plot[BesselI[0, x], {x, 0, 5}]
The special case of half-integer index is expanded using Rayleigh's formulas:
BesselI[3/2, x]
Integer orders are not expanded and remain symbolic:
BesselI[1, z]